Mahan Tajrobehkar | Searcharxiv

arXiv2025

MFGLib: A Library for Mean-Field Games

Mean-field games (MFGs) are limiting models to approximate $N$-player games, with a number of applications. Despite the ever-growing numerical literature on computation of MFGs, there is no library that allows researchers and practitioners to easily create and solve their own MFG problems. The purpose of this document is to introduce MFGLib, an open-source Python library for solving general MFGs with a user-friendly and customizable interface. It serves as a handy tool for creating and analyzing generic MFG environments, along with embedded auto-tuners for all implemented algorithms. The package is distributed under the MIT license and the source code and documentation can be found at https://github.com/radar-research-lab/MFGLib/.

cs.GT↗

arXiv2022

Escaping Saddle Points Efficiently with Occupation-Time-Adapted Perturbations

Motivated by the super-diffusivity of self-repelling random walk, which has roots in statistical physics, this paper develops a new perturbation mechanism for optimization algorithms. In this mechanism, perturbations are adapted to the history of states via the notion of occupation time. After integrating this mechanism into the framework of perturbed gradient descent (PGD) and perturbed accelerated gradient descent (PAGD), two new algorithms are proposed: perturbed gradient descent adapted to occupation time (PGDOT) and its accelerated version (PAGDOT). PGDOT and PAGDOT are shown to converge to second-order stationary points at least as fast as PGD and PAGD, respectively, and thus they are guaranteed to avoid getting stuck at non-degenerate saddle points. The theoretical analysis is corroborated by empirical studies in which the new algorithms consistently escape saddle points and outperform not only their counterparts, PGD and PAGD, but also other popular alternatives including stochastic gradient descent, Adam, AMSGrad, and RMSProp.

math.OC↗